I have made a USB boot-drive for Linux Mint 14 32-bit. There is a 1.5 GB Persistent file on it, though I haven't really found out what it is used for yet.

I had installed some new packages, but when I clicked the icon of Blender 3D and selected 'add to panel', it did that but then suddenly all the quick-launch icons disappeared and my screen froze. I had to cut the power off to reboot. It booted into the initial state of Linux Mint, before all the changes and new package installs.

Is there a way for me to install Linux packages directly onto my USB drive, so that I can have my fully customized Linux Mint on-the-go?

Some things can be installed most cant. You are still using a live image after all. Persistence is best used for settings changes and files, these are kept in the virtual "home" within the persistence file. When programs are installed they have to recreate the root file system again within the persistence file, but, quite a few cause problems because these progs have to be reread back into the virtual root system which is in memory. Causing all kinds of fun!

Adding progs also increase the likelihood of the casper-rw file becoming corrupt.